Under separability or the sufficiently scattered condition on nonnegative factors and full-rank conditions on core slices or unfoldings, nonnegative Tucker decompositions are essentially unique and are recovered by minimizing core volume.
Uncovering audio patterns in music with Nonnegative Tucker Decomposition for structural segmentation
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abstract
Recent work has proposed the use of tensor decomposition to model repetitions and to separate tracks in loop-based electronic music. The present work investigates further on the ability of Nonnegative Tucker Decompositon (NTD) to uncover musical patterns and structure in pop songs in their audio form. Exploiting the fact that NTD tends to express the content of bars as linear combinations of a few patterns, we illustrate the ability of the decomposition to capture and single out repeated motifs in the corresponding compressed space, which can be interpreted from a musical viewpoint. The resulting features also turn out to be efficient for structural segmentation, leading to experimental results on the RWC Pop data set which are potentially challenging state-of-the-art approaches that rely on extensive example-based learning schemes.
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2025 1verdicts
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Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory
Under separability or the sufficiently scattered condition on nonnegative factors and full-rank conditions on core slices or unfoldings, nonnegative Tucker decompositions are essentially unique and are recovered by minimizing core volume.